Introduction to Variables

What is a Variable?

In math, we sometimes do not know the exact value of a number, or we are working with a quantity that can change. When this happens, we use a letter to stand in for that unknown number. This letter is called a variable.

The most common variables you will see are $x$, $y$, and $n$, but you can use any letter of the alphabet!

Writing Expressions with Variables

An expression is a mathematical phrase that combines numbers, operation symbols (like $+$, $-$, $\times$, $\div$), and variables. It does not have an equals sign.

You can translate word phrases into math expressions by looking for clue words:

• Addition: "more than", "sum", "increased by"
• Subtraction: "less than", "difference", "decreased by"
• Multiplication: "times", "product", "multiply by"

Example 1: If $n$ is a number, write an expression for "6 more than $n$".

• "More than" tells us to add.
• The expression is: $n + 6$

Example 2: A rule says "multiply by 4 then subtract 1." Write it using $x$.

• First, multiply $x$ by 4: $x \times 4$
• Then, subtract 1: $x \times 4 - 1$

Evaluating Expressions

To evaluate an expression means to find its exact value when you are given a specific number for the variable. You simply substitute (swap) the letter with the number and do the math!

Example 3: Evaluate $n \times 3 + 2$ when $n = 5$.

1. Substitute: Replace the letter $n$ with the number $5$. $5 \times 3 + 2$
2. Multiply: Follow the order of operations and do the multiplication first. $15 + 2$
3. Add: $17$

So, when $n = 5$, the value of the expression is $17$.

Summary

• Variable: A letter (like $n$ or $x$) used to represent an unknown number.
• Expression: A math phrase with numbers, variables, and operations (e.g., $x + 5$).
• Evaluate: To replace a variable with a number and calculate the final answer.